Synchronisation of almost all trajectories of a random dynamical system
Dynamical Systems
2016-01-12 v2
Abstract
It has been shown by Le Jan that, given a memoryless-noise random dynamical system together with an ergodic distribution for the associated Markov transition probabilities, if the support of the ergodic distribution admits locally asymptotically stable trajectories, then there is a random attracting set consisting of finitely many points, whose basin of forward-time attraction includes a random full measure open set. In this paper, we present necessary and sufficient conditions for this attracting set to be a singleton; our result does not require the state space to be compact, but holds on general Lusin metric spaces.
Keywords
Cite
@article{arxiv.1511.08831,
title = {Synchronisation of almost all trajectories of a random dynamical system},
author = {Julian Newman},
journal= {arXiv preprint arXiv:1511.08831},
year = {2016}
}